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[freedom97]

1. One way to show that a statement is not a good definition is to find a ____. (1 point)
converse
conditional
biconditional
counterexample

2. Which choice shows a true conditional with a correctly identified hypothesis and conclusion? (1 point)
If next month is January, then this month is the last of the year.
Hypothesis: This month is the last of the year.
Conclusion: Next month is January.
Next month is February, so this month is the last month of the year.
Hypothesis: Next month is February.
Conclusion: This month is the last of the year.
Next month is February, so this month is the last month of the year.
Hypothesis: This month is the last of the year.
Conclusion: Next month is February.
If next month is January, then this month is the last of the year.
Hypothesis: Next month is January.
Conclusion: This month is the last of the year.

4. Is the following definition of perpendicular reversible? If yes, write it as a true biconditional.
Two lines that intersect at right angles are perpendicular. (1 point)
The statement is not reversible.
Yes; if two lines intersect at right angles, then they are perpendicular.
Yes; if two lines are perpendicular, then they intersect at right angles.
Yes; two lines intersect at right angles if (and only if) they are perpendicular.

5. Which biconditional is not a good definition? (1 point)
A whole number is odd if and only if the number is not divisible by 2.
An angle is straight if and only if its measure is 180°.
A whole number is even if and only if it is divisible by 2.
A ray is a bisector of an angle if and only if it splits the angle into two angles.

6. Use the Law of Detachment to draw a conclusion from the two given statements. If not possible, write not possible.

If I miss a basketball practice, then I cannot play in the upcoming game.
(1 point)
I missed basketball practice.
I did not miss basketball practice.
If I miss the upcoming basketball game, then I missed practice.
not possible

7. Name the Property of Congruence that justifies this statement:

(1 point)
Transitive Property
Symmetric Property
Reflexive Property
none of these

8. What is a counterexample for the conjecture?

Conjecture: Any number that is divisible by 4 is also divisible by 8.
(1 point)
24
40
12
26

9. Use the Law of Syllogism to draw a conclusion from the two given statements.

If two lines intersect and form right angles, then the lines are perpendicular.
If two lines are perpendicular, then they intersect and form 90° angles.

(1 point)
The lines intersect and form 90° angles.
If two lines do not intersect and form 90° angles, then they do not form right angles.
The lines are perpendicular.
If two lines intersect and form right angles, then they intersect and form 90° angles.

10. For the following true conditional statement, write the converse. If the converse is also true, combine the statements as a biconditional.
If x = 3, then x2 = 9.

(1 point)
If x2 = 9, then x = 3. True; x2 = 9 if and only if x = 3.
If x2 = 3, then x = 9. False.
If x2 = 9, then x = 3. True; x = 3 if and only if x2 = 9.
If x2 = 9, then x = 3. False.